Chapter 5 - Section 5.2 - Sum and Difference Formulas - 5.2 Problem Set - Page 288: 11

$= (2-\sqrt(3))$

$tan(15) = tan(60-45)$ $= \frac{[tan(60)-tan(45)]}{[1+tan(60)\times tan(45)]}$ $=\frac{[\sqrt(3)-1]}{[1+\sqrt(3)*1]}$ Multiply numerator and denominator by $(1-\sqrt(3))$ to get $= [-(1-\sqrt(3))^2]/(1-3)$ $= (1-2\sqrt(3)+3)/2$ $= (4-2\sqrt(3))/2$ $= (2-\sqrt(3))$